5 Search Results for "Valiron, Benoît"


Document
A Curry-Howard Correspondence for Linear, Reversible Computation

Authors: Kostia Chardonnet, Alexis Saurin, and Benoît Valiron

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)


Abstract
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of clauses is enough to ensure reversibility. The language allows to represent any Primitive Recursive Function. We then give a Curry-Howard correspondence with the logic μMALL: linear logic extended with least fixed points allowing inductive statements. The critical part of our work is to show how primitive recursion yields circular proofs that satisfy μMALL validity criterion and how the language simulates the cut-elimination procedure of μMALL.

Cite as

Kostia Chardonnet, Alexis Saurin, and Benoît Valiron. A Curry-Howard Correspondence for Linear, Reversible Computation. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{chardonnet_et_al:LIPIcs.CSL.2023.13,
  author =	{Chardonnet, Kostia and Saurin, Alexis and Valiron, Beno\^{i}t},
  title =	{{A Curry-Howard Correspondence for Linear, Reversible Computation}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.13},
  URN =		{urn:nbn:de:0030-drops-174747},
  doi =		{10.4230/LIPIcs.CSL.2023.13},
  annote =	{Keywords: Reversible Computation, Linear Logic, Curry-Howard}
}
Document
LO_v-Calculus: A Graphical Language for Linear Optical Quantum Circuits

Authors: Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, and Benoît Valiron

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
We introduce the LO_v-calculus, a graphical language for reasoning about linear optical quantum circuits with so-called vacuum state auxiliary inputs. We present the axiomatics of the language and prove its soundness and completeness: two LO_v-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LO_v-calculus. We give a confluent and terminating rewrite system to rewrite any polarisation-preserving LO_v-circuit into a unique triangular normal form, inspired by the universal decomposition of Reck et al. (1994) for linear optical quantum circuits.

Cite as

Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, and Benoît Valiron. LO_v-Calculus: A Graphical Language for Linear Optical Quantum Circuits. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{clement_et_al:LIPIcs.MFCS.2022.35,
  author =	{Cl\'{e}ment, Alexandre and Heurtel, Nicolas and Mansfield, Shane and Perdrix, Simon and Valiron, Beno\^{i}t},
  title =	{{LO\underlinev-Calculus: A Graphical Language for Linear Optical Quantum Circuits}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.35},
  URN =		{urn:nbn:de:0030-drops-168334},
  doi =		{10.4230/LIPIcs.MFCS.2022.35},
  annote =	{Keywords: Quantum Computing, Graphical Language, Linear Optical Circuits, Linear Optical Quantum Computing, Completeness}
}
Document
Concrete Categorical Model of a Quantum Circuit Description Language with Measurement

Authors: Dongho Lee, Valentin Perrelle, Benoît Valiron, and Zhaowei Xu

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)


Abstract
In this paper, we introduce dynamic lifting to a quantum circuit-description language, following the Proto-Quipper language approach. Dynamic lifting allows programs to transfer the result of measuring quantum data - qubits - into classical data - booleans -. We propose a type system and an operational semantics for the language and we state safety properties. Next, we introduce a concrete categorical semantics for the proposed language, basing our approach on a recent model from Rios&Selinger for Proto-Quipper-M. Our approach is to construct on top of a concrete category of circuits with measurements a Kleisli category, capturing as a side effect the action of retrieving classical content out of a quantum memory. We then show a soundness result for this semantics.

Cite as

Dongho Lee, Valentin Perrelle, Benoît Valiron, and Zhaowei Xu. Concrete Categorical Model of a Quantum Circuit Description Language with Measurement. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 51:1-51:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{lee_et_al:LIPIcs.FSTTCS.2021.51,
  author =	{Lee, Dongho and Perrelle, Valentin and Valiron, Beno\^{i}t and Xu, Zhaowei},
  title =	{{Concrete Categorical Model of a Quantum Circuit Description Language with Measurement}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{51:1--51:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.51},
  URN =		{urn:nbn:de:0030-drops-155627},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.51},
  annote =	{Keywords: Categorical semantics, Operational semantics, Quantum circuit description language}
}
Document
Geometry of Interaction for ZX-Diagrams

Authors: Kostia Chardonnet, Benoît Valiron, and Renaud Vilmart

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machine-based asynchronous model of both pure ZX-Calculus and its extension to mixed processes. We also show how to connect this new semantics to the usual standard interpretation of ZX-diagrams. This model allows us to have a new look at what ZX-diagrams compute, and give a more local, operational view of the semantics of ZX-diagrams.

Cite as

Kostia Chardonnet, Benoît Valiron, and Renaud Vilmart. Geometry of Interaction for ZX-Diagrams. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{chardonnet_et_al:LIPIcs.MFCS.2021.30,
  author =	{Chardonnet, Kostia and Valiron, Beno\^{i}t and Vilmart, Renaud},
  title =	{{Geometry of Interaction for ZX-Diagrams}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.30},
  URN =		{urn:nbn:de:0030-drops-144701},
  doi =		{10.4230/LIPIcs.MFCS.2021.30},
  annote =	{Keywords: Quantum Computation, Linear Logic, ZX-Calculus, Geometry of Interaction}
}
Document
Invited Talk
A Linear Logical Framework in Hybrid (Invited Talk)

Authors: Amy P. Felty

Published in: LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)


Abstract
We present a linear logical framework implemented within the Hybrid system [Amy P. Felty and Alberto Momigliano, 2012]. Hybrid is designed to support the use of higher-order abstract syntax for representing and reasoning about formal systems, implemented in the Coq Proof Assistant. In this work, we extend the system with two linear specification logics, which provide infrastructure for reasoning directly about object languages with linear features. We originally developed this framework in order to address the challenges of reasoning about the type system of a quantum lambda calculus. In particular, we started by considering the Proto-Quipper language [Neil J. Ross, 2015], which contains the core of Quipper [Green et al., 2013; Peter Selinger and Benoît Valiron, 2006]. Quipper is a relatively new quantum programming language under active development with a linear type system. We have completed a formal proof of type soundness for Proto-Quipper [Mohamed Yousri Mahmoud and Amy P. Felty, 2018]. Our current work includes extending this work to other properties of Proto-Quipper, reasoning about other quantum programming languages [Mohamed Yousri Mahmoud and Amy P. Felty, 2018], and reasoning about other languages such as the meta-theory of low-level abstract machine code. We are also interested in applying this framework to applications outside the domain of meta-theory of programming languages and have focused on two areas - formal reasoning about the proof theory of focused linear sequent calculi and modeling biological processes as transition systems and proving properties about them. We found that a slight extension of the initial linear specification logic allowed us to provide succinct encodings and facilitate reasoning in these new domains. We illustrate by discussing a model of breast cancer progression as a set of transition rules and proving properties about this model [Joëlle Despeyroux et al., 2018]. Current work also includes modeling stem cells as they mature into different types of blood cells. This work illustrates the use of Hybrid as a meta-logical framework for fast prototyping of logical frameworks, which is achieved by defining inference rules of a specification logic inductively in Coq and building a library of definitions and lemmas used to reason about a class of object logics. Our focus here is on linear specification logics and their applications.

Cite as

Amy P. Felty. A Linear Logical Framework in Hybrid (Invited Talk). In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{felty:LIPIcs.FSCD.2019.2,
  author =	{Felty, Amy P.},
  title =	{{A Linear Logical Framework in Hybrid}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{2:1--2:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.2},
  URN =		{urn:nbn:de:0030-drops-105099},
  doi =		{10.4230/LIPIcs.FSCD.2019.2},
  annote =	{Keywords: Logical frameworks, proof assistants, linear logic}
}
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